https://www.khanacademy.org/math/geometry-home/right-triangles-topic/intro-to-the-trig-ratios-geo/v/basic-trigonometry 2023-04-19T21:28:53.788177796Z Intro to the trigonometric ratios Sin, cos, and tan are trigonometric ratios that relate the angles and sides of right triangles. Sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, and tan is the ratio of the opposite side to the adjacent side. They are often written as sin(x), cos(x), and tan(x), where x is an angle in radians or degrees. Sal Khan video https://cdn.kastatic.org/googleusercontent/92f-z9P3xlQjRzRxw0jbZbOpAzwmjBTqS0jsZc35x2__HYRgkdQOu9L4be8LG41cffV9nRfKOwGzLFG8nw-Oi_en Intro to the trigonometric ratios Sin, cos, and tan are trigonometric ratios that relate the angles and sides of right triangles. Sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, and tan is the ratio of the opposite side to the adjacent side. They are often written as sin(x), cos(x), and tan(x), where x is an angle in radians or degrees. https://cdn.kastatic.org/ka-youtube-converted/Jsiy4TxgIME.mp4/Jsiy4TxgIME.mp4 557 Basic trigonometry https://www.khanacademy.org/math/board-preparation-maharashtra-math-10/x20d33f0422cd733e:week-3-board-prep-maharashtra/x20d33f0422cd733e:trigonometry/v/intro-to-heights-and-distances 2020-08-19T18:08:11Z Intro to heights and distances Let's get introduced to heights and distances. Let's learn the meaning of the terms - 'line of sight', 'angle of elevation', and 'angle of depression'. Aanand Srinivas video https://cdn.kastatic.org/googleusercontent/rou31Q6o1bYVnUOnOffSv4-ikH4zYKR6PEk51p7ZS5yKyqSqwiNqKoUlTT4CP4jttDCT01YiXmSmf7ixbwSfbPMA Intro to heights and distances Let's get introduced to heights and distances. Let's learn the meaning of the terms - 'line of sight', 'angle of elevation', and 'angle of depression'. https://cdn.kastatic.org/ka-youtube-converted/TgQs7k5p2Ag.mp4/TgQs7k5p2Ag.mp4 767 Basic trigonometry https://www.khanacademy.org/math/geometry-home/right-triangles-topic/special-right-triangles/v/45-45-90-triangles 2023-05-12T21:01:01.897246564Z Special right triangles intro (part 1) A 45-45-90 triangle is a special type of right triangle, where the ratio of the lengths of the sides of a 45-45-90 triangle is always 1:1:√2, meaning that if one leg is x units long, then the other leg is also x units long, and the hypotenuse is x√2 units long. Sal Khan video https://cdn.kastatic.org/googleusercontent/SBPUnFjSSvdka1RgDmNi0p59ZQtA4NH5yWRK8db9FuRrjMxB7XZNhHpH9mFCSvnyP9zo2C3n-zU23q7huLagxx8 Special right triangles intro (part 1) A 45-45-90 triangle is a special type of right triangle, where the ratio of the lengths of the sides of a 45-45-90 triangle is always 1:1:√2, meaning that if one leg is x units long, then the other leg is also x units long, and the hypotenuse is x√2 units long. https://cdn.kastatic.org/ka-youtube-converted/tSHitjFIjd8.mp4/tSHitjFIjd8.mp4 570 Basic trigonometry https://www.khanacademy.org/math/geometry-home/right-triangles-topic/special-right-triangles/v/intro-to-30-60-90-triangles 2023-05-12T21:01:01.897246564Z Special right triangles intro (part 2) A 30-60-90 triangle is a special right triangle with angles of 30, 60, and 90 degrees. It has properties similar to the 45-45-90 triangle. The side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is the length of the short leg times the square root of three. Alternatively, the ratio of the sides is 1 : √3 : 2. Sal Khan video https://cdn.kastatic.org/googleusercontent/4zW0dP4es71plw0j7IvG2zH6YF0ZS4Bk8V6hZazoH3jbqT2p_1YB5SDP5XWp3qZkHUdAT2P95grM7v3c5KGec6s Special right triangles intro (part 2) A 30-60-90 triangle is a special right triangle with angles of 30, 60, and 90 degrees. It has properties similar to the 45-45-90 triangle. The side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is the length of the short leg times the square root of three. Alternatively, the ratio of the sides is 1 : √3 : 2. https://cdn.kastatic.org/ka-youtube-converted/Qwet4cIpnCM.mp4/Qwet4cIpnCM.mp4 579 Basic trigonometry https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/v/30-60-90-triangle-example-problem 2021-03-30T19:55:56Z 30-60-90 triangle example problem Using what we know about 30-60-90 triangles to solve what at first seems to be a challenging problem Sal Khan video https://cdn.kastatic.org/googleusercontent/UaiP-JD6_uAgur8B076pwq4uGj1vDwaVMIDqNcAu68jkBzI7Z5OnGvknFgaKNZVuoDtt6QGLOHJxqhMxehjsMlWV 30-60-90 triangle example problem Using what we know about 30-60-90 triangles to solve what at first seems to be a challenging problem https://cdn.kastatic.org/ka-youtube-converted/dgHksfBFbjk.mp4/dgHksfBFbjk.mp4 400 Basic trigonometry https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-a-side/v/example-trig-to-solve-the-sides-and-angles-of-a-right-triangle 2021-06-30T17:32:38Z Solving for a side in right triangles with trigonometry Sal is given a right triangle with an acute angle of 65° and a leg of 5 units, and he uses trigonometry to find the two missing sides. Sal Khan video https://cdn.kastatic.org/googleusercontent/X0ECxxkRbmZu7H78vm4EbH8BRKYqPBGlzkuAdFqDsmG5d33yLEW3qY54S02C0-YF6OUMI-SPnXfHJYAyuzICHfCYJQ Solving for a side in right triangles with trigonometry Sal is given a right triangle with an acute angle of 65° and a leg of 5 units, and he uses trigonometry to find the two missing sides. https://cdn.kastatic.org/ka-youtube-converted/l5VbdqRjTXc.mp4/l5VbdqRjTXc.mp4 424 Basic trigonometry https://www.khanacademy.org/math/geometry-home/geometry-volume-surface-area/heron-formula-tutorial/v/heron-s-formula 2020-08-25T18:06:03Z Heron's formula Using Heron's Formula to determine the area of a triangle while only knowing the lengths of the sides Sal Khan video https://cdn.kastatic.org/googleusercontent/yoFDg3hgOeccTlrdVdadCkI70dwwbRa5rdjmKatYCkDVuLJRSfOYvwJCwj-wgmaTx5WD7zTb2gICFbPGqOoZZyM Heron's formula Using Heron's Formula to determine the area of a triangle while only knowing the lengths of the sides https://cdn.kastatic.org/ka-youtube-converted/-YI6UC4qVEY.mp4/-YI6UC4qVEY.mp4 283 Basic trigonometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:solving-general-triangles/v/law-of-cosines-word-problem 2021-04-07T10:59:32Z Trig word problem: stars Sal solves a word problem about the distance between stars using the law of cosines. Sal Khan video https://cdn.kastatic.org/googleusercontent/6yEMY9OWtEyiLbzaRsnCgrSk_oQk6NIgIkzFigA1Ec2YD-QcpYPZqiafaLsibpOVhSP6Cv6LBAjQWAApv7aTsBvy Trig word problem: stars Sal solves a word problem about the distance between stars using the law of cosines. https://cdn.kastatic.org/ka-youtube-converted/6kGi1dvGZNY.mp4/6kGi1dvGZNY.mp4 360 Basic trigonometry https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-a-side/a/unknown-side-in-right-triangle-w-trig 2025-02-11T16:42:34.189704851Z Solving for a side in right triangles with trigonometry Learn how to use trig functions to find an unknown side length in a right triangle. article https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/a/finding-trig-ratios-in-right-triangles 2022-09-10T02:03:40.164764806Z Trigonometric ratios in right triangles Learn how to find the sine, cosine, and tangent of angles in right triangles. article https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/a/angles-of-elevation-and-depression 2022-09-10T02:03:40.164764806Z Angles of elevation and depression Learn what  the terms angle of elevation and angle of depression mean. The words may be big but their meaning is pretty basic! article https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/e/trigonometry_1 2026-04-01T11:24:50.133517701Z Trigonometric ratios in right triangles Given the side lengths of a right triangle, find the sine, cosine, or tangent of one of the acute angles. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/e/pythagorean_theorem_2 2025-12-30T07:05:15.972746521Z Special right triangles Use the Pythagorean theorem to discover patterns in 30°-60°-90° and 45°-45°-90° triangles. Ben Alpert exercise https://www.khanacademy.org/math/ka-math-class-9/x152b0968b8680a8d:heron-s-formula-ncert-new/x152b0968b8680a8d:area-of-triangle-by-heron-s-formula/e/understanding-heron-s-formula 2024-06-10T11:27:45.483509161Z Understanding Heron's formula This exercise is a replica of 10.1 exercise which was do-all, now this is curated for new ncert and is do-4 Devashish Phadnis exercise https://www.khanacademy.org/math/class-9-geometry-od/x0a98afb01410c41a:mensuration/x0a98afb01410c41a:area-of-triangles/e/finding-area-of-triangle-using-heron-s-formula 2026-03-07T07:20:41.87360937Z Finding area of triangle using Heron's formula part 1 We will find the area of triangle using Heron's formula. anmol exercise https://www.khanacademy.org/math/ka-math-class-9/x152b0968b8680a8d:heron-s-formula-ncert-new/x152b0968b8680a8d:area-of-triangle-by-heron-s-formula/e/finding-area-of-triangle-part-2 2024-05-16T12:18:34.840009131Z Finding area of triangle part 2 Using herons formula a little difficult problem. Devashish Phadnis exercise